where \( {f_{min}} \)  is the global minimum of \( f(\theta ) \) , and \( 0 < c \le L \) . It is noted that this assumption only requires the function to attain a global minimum (more detailed discussion in [1]}).
Also:
\({\mathbb {E}_{{\xi _t}}}[{\left\Vert  {g({\theta _t},{\xi _t})} \right\Vert ^2}] \le {M} + {M_G}{\left\Vert  {\nabla f({\theta _t})} \right\Vert ^2} \,\, \text{ for } \,\, t \in \mathbb {N},\) 
